Question

The compound titanium oxide occurs in the mineral rutile. Use the periodic table to predict the formula for titanium oxide, given the formula of zirconium oxide, \(\mathrm{ZrO}_{2}\).

Short answer

The formula for titanium oxide is \(\mathrm{TiO}_2\).

Step-by-step solution

Understand the Given Formula

The formula given is for zirconium oxide, \( \mathrm{ZrO}_2 \). This indicates that for every zirconium atom, there are two oxygen atoms.

Identify the Oxidation State

Zirconium (Zr) typically has an oxidation state of +4 since in \( \mathrm{ZrO}_2 \), each oxygen has an oxidation state of -2. Thus, the zirconium balances the charge with +4.

Apply to Titanium

Titanium is in the same group as zirconium in the periodic table, which means it commonly exhibits similar oxidation states. Like zirconium, titanium often has an oxidation state of +4.

Derive the Titanium Oxide Formula

Using the +4 oxidation state of titanium, mimic the formula pattern of \(\mathrm{ZrO}_2\) for titanium. Thus, the formula would be \(\mathrm{TiO}_2\), since two oxygen atoms at -2 each will balance the +4 oxidation state of a single titanium atom.

Key concepts

Titanium Oxide

Titanium oxide is a chemical compound composed of titanium and oxygen. In the mineral world, it is most commonly found in the form known as rutile. The formula for titanium oxide is derived by understanding the oxidation state of the titanium and oxygen atoms involved. Titanium, with its shiny and durable properties, bonds with oxygen to form a stable compound. * The chemical formula for titanium oxide is \(\text{TiO}_2\), indicating one titanium atom and two oxygen atoms. * It often appears in a white powdered form and is widely used in various industries such as paints, sunscreens, and food coloring due to its opacity and brightness. By deriving this formula, we recognize the balance of charges between the elements, which creates this stable compound seen in nature and industry.

Oxidation State

Understanding oxidation states is crucial in predicting chemical formulas. The oxidation state can be thought of as an atom's "charge" and indicates how many electrons an atom can gain, lose, or share when forming a compound. * Oxygen typically has an oxidation state of -2, meaning it tends to gain two electrons. * In compounds, the sum of all oxidation states must equal zero for it to be neutral. For titanium oxide, the titanium atom commonly exhibits an oxidation state of +4. This means it can "balance out" the two oxygen atoms each with a -2 oxidation state. By doing this, the charges equate to zero, making \(\text{TiO}_2\) a stable compound.

Periodic Table Analysis

The periodic table is not just a list of elements; it organizes them in a way that reflects their properties and relationships. Elements in the same group, or column, have similar chemical behaviors due to the number of electrons in their outer shell. * Both titanium and zirconium are in Group 4 of the periodic table, meaning they often display a +4 oxidation state. * This similarity is because of their atomic structure, which influences how they bond with other elements. When we compare zirconium oxide \(\text{ZrO}_2\) with titanium oxide \(\text{TiO}_2\), the period table helps us understand that these compounds are similar thanks to their elemental properties. This methodological use of the periodic table allows for accurate chemical formula predictions across elements within the same group.